Question 183
In the left-lower corner $1 \times 1$ cell of the $m \times n$ board ($m, n \geq 3$) there is a black chip, and in the left-upper and right-lower cells, there are white chips. In his move, Petrik can move the black chip to the adjacent by side cell twice in a row, and Vasyl can either move one of the white chips to the adjacent by side cell twice in a row or move each of the two white chips separately to the adjacent by side cells. Chips can not be placed on fields that have already been visited by a chip of another color. Vasyl wins if after some point both white chips end up in the same cell. If Vasyl wants to win, and Petrik wants not to give him such an opportunity, then under what conditions on $m$ and $n$ does Vasily win? Petrik moves first.
*(Arseniy Nikolaev)*
*(Arseniy Nikolaev)*